def statistics_quadratic_time_mmd (m,dim,difference): from shogun.Features import RealFeatures from shogun.Features import MeanShiftDataGenerator from shogun.Kernel import GaussianKernel, CustomKernel from shogun.Statistics import QuadraticTimeMMD from shogun.Statistics import BOOTSTRAP, MMD2_SPECTRUM, MMD2_GAMMA, BIASED, UNBIASED from shogun.Mathematics import Statistics, IntVector, RealVector, Math # init seed for reproducability Math.init_random(1) # number of examples kept low in order to make things fast # streaming data generator for mean shift distributions gen_p=MeanShiftDataGenerator(0, dim); gen_q=MeanShiftDataGenerator(difference, dim); # stream some data from generator feat_p=gen_p.get_streamed_features(m); feat_q=gen_q.get_streamed_features(m); # set kernel a-priori. usually one would do some kernel selection. See # other examples for this. width=10; kernel=GaussianKernel(10, width); # create quadratic time mmd instance. Note that this constructor # copies p and q and does not reference them mmd=QuadraticTimeMMD(kernel, feat_p, feat_q); # perform test: compute p-value and test if null-hypothesis is rejected for # a test level of 0.05 alpha=0.05; # using bootstrapping (slow, not the most reliable way. Consider pre- # computing the kernel when using it, see below). # Also, in practice, use at least 250 iterations mmd.set_null_approximation_method(BOOTSTRAP); mmd.set_bootstrap_iterations(3); p_value_boot=mmd.perform_test(); # reject if p-value is smaller than test level #print "bootstrap: p!=q: ", p_value_boot<alpha # using spectrum method. Use at least 250 samples from null. # This is consistent but sometimes breaks, always monitor type I error. # See tutorial for number of eigenvalues to use . # Only works with BIASED statistic mmd.set_statistic_type(BIASED); mmd.set_null_approximation_method(MMD2_SPECTRUM); mmd.set_num_eigenvalues_spectrum(3); mmd.set_num_samples_sepctrum(250); p_value_spectrum=mmd.perform_test(); # reject if p-value is smaller than test level #print "spectrum: p!=q: ", p_value_spectrum<alpha # using gamma method. This is a quick hack, which works most of the time # but is NOT guaranteed to. See tutorial for details. # Only works with BIASED statistic mmd.set_statistic_type(BIASED); mmd.set_null_approximation_method(MMD2_GAMMA); p_value_gamma=mmd.perform_test(); # reject if p-value is smaller than test level #print "gamma: p!=q: ", p_value_gamma<alpha # compute tpye I and II error (use many more trials in practice). # Type I error is not necessary if one uses bootstrapping. We do it here # anyway, but note that this is an efficient way of computing it. # Also note that testing has to happen on # difference data than kernel selection, but the linear time mmd does this # implicitly and we used a fixed kernel here. mmd.set_null_approximation_method(BOOTSTRAP); mmd.set_bootstrap_iterations(5); num_trials=5; type_I_errors=RealVector(num_trials); type_II_errors=RealVector(num_trials); inds=int32(array([x for x in range(2*m)])) # numpy p_and_q=mmd.get_p_and_q(); # use a precomputed kernel to be faster kernel.init(p_and_q, p_and_q); precomputed=CustomKernel(kernel); mmd.set_kernel(precomputed); for i in range(num_trials): # this effectively means that p=q - rejecting is tpye I error inds=random.permutation(inds) # numpy permutation precomputed.add_row_subset(inds); precomputed.add_col_subset(inds); type_I_errors[i]=mmd.perform_test()>alpha; precomputed.remove_row_subset(); precomputed.remove_col_subset(); # on normal data, this gives type II error type_II_errors[i]=mmd.perform_test()>alpha; return type_I_errors.get(),type_I_errors.get(),p_value_boot,p_value_spectrum,p_value_gamma,